Differentiable Maximum Likelihood Noise Estimation for Quantum Error Correction

• URL: http://arxiv.org/abs/2602.19722v1
• Date: Mon, 23 Feb 2026 11:20:23 GMT
• Title: Differentiable Maximum Likelihood Noise Estimation for Quantum Error Correction
• Authors: Hanyan Cao, Dongyang Feng, Cheng Ye, Feng Pan,
• Abstract summary: We introduce a differentiable Likelihood Estimation framework that enables exact, efficient, and fully differentiable Maximum of syndrome log-likelihoods.<n>Our approach yields provably optimal, decoder-independent error priors by directly maximizing the syndrome likelihood.
• Score: 3.1257175823346905
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Accurate noise estimation is essential for fault-tolerant quantum computing, as decoding performance depends critically on the fidelity of the circuit-level noise parameters. In this work, we introduce a differentiable Maximum Likelihood Estimation (dMLE) framework that enables exact, efficient, and fully differentiable computation of syndrome log-likelihoods, allowing circuit-level noise parameters to be optimized directly via gradient descent. Leveraging the exact Planar solver for repetition codes and a novel, simplified Tensor Network (TN) architecture combined with optimized contraction path finding for surface codes, our method achieves tractable and fully differentiable likelihood evaluation even for distance 5 surface codes with up to 25 rounds. Our method recovers the underlying error probabilities with near-exact precision in simulations and reduces logical error rates by up to 30.6(3)% for repetition codes and 8.1(2)% for surface codes on experimental data from Google's processor compared to previous state-of-the-art methods: correlation analysis and Reinforcement Learning (RL) methods. Our approach yields provably optimal, decoder-independent error priors by directly maximizing the syndrome likelihood, offering a powerful noise estimation and control tool for unlocking the full potential of current and future error-corrected quantum processors.

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